Stress, Strain and Young's Modulus

Stress is force per unit area - strain is the deformation of a solid due to stress. EngineeringToolBox-Resources,ToolsandBasicInformationforEngineeringandDesignofTechnicalApplications! Stress,StrainandYoung'sModulusStressisforceperunitarea-strainisthedeformationofasolidduetostress.SponsoredLinksStressStressistheratioofappliedforceFtoacrosssectionarea-definedas"forceperunitarea".tensilestress-stressthattendstostretchorlengthenthematerial-actsnormaltothestressedareacompressivestress-stressthattendstocompressorshortenthematerial-actsnormaltothestressedareashearingstress-stressthattendstoshearthematerial-actsinplanetothestressedareaatright-anglestocompressiveortensilestressTensileorCompressiveStress-NormalStressTensileorcompressivestressnormaltotheplaneisusuallydenoted"normalstress"or"directstress"andcanbeexpressedasσ=Fn/A                    (1)whereσ=normalstress(Pa(N/m2),psi(lbf/in2))Fn=normalforceactingperpendiculartothearea(N,lbf)A=area(m2,in2)akipisanimperialunitofforce-itequals1000lbf(pounds-force)1kip=4448.2216Newtons(N)=4.4482216kiloNewtons(kN)Anormalforceactsperpendiculartoareaandisdevelopedwheneverexternalloadstendstopushorpullthetwosegmentsofabody.Example-TensileForceactingonaRodAforceof10kNisactingonacircularrodwithdiameter10mm.Thestressintherodcanbecalculatedasσ=(10103N) /(π((1010-3m)/2)2)  =127388535(N/m2)   =127 (MPa)Example-ForceactingonaDouglasFirSquarePostAcompressiveloadof30000lbisactingonshortsquare6x6inpostofDouglasfir.Thedressedsizeofthepostis5.5x5.5inandthecompressivestresscanbecalculatedasσ=(30000lb) /((5.5in)(5.5in))  =991(lb/in2,psi)ShearStressStressparalleltoaplaneisusuallydenotedas"shearstress"andcanbeexpressedasτ=Fp/A                  (2)whereτ=shearstress(Pa(N/m2),psi(lbf/in2))Fp=shearforceintheplaneofthearea(N,lbf)A=area(m2,in2)Ashearforceliesintheplaneofanareaandisdevelopedwhenexternalloadstendtocausethetwosegmentsofabodytoslideoveroneanother.Strain(Deformation)Strainisdefinedas"deformationofasolidduetostress". Normalstrain-elongationorcontractionofalinesegmentShearstrain-changeinanglebetweentwolinesegmentsoriginallyperpendicularNormalstrainandcanbeexpressedasε=dl/lo  =σ/E                 (3)wheredl=changeoflength(m,in)lo=initiallength(m,in)ε=strain-unit-lessE=Young'smodulus(ModulusofElasticity)(Pa,(N/m2),psi(lbf/in2))Young'smoduluscanbeusedtopredicttheelongationorcompressionofanobjectwhenexposedtoaforceNotethatstrainisadimensionlessunitsinceitistheratiooftwolengths.Butitalsocommonpracticetostateitastheratiooftwolengthunits-likem/morin/in.Poisson'sratioistheratioofrelativecontractionstrainExample-StressandChangeofLengthTherodintheexampleaboveis2mlongandmadeofsteelwithModulusofElasticity200GPa(200109N/m2).Thechangeoflengthcanbecalculatedbytransforming(3)to dl=σlo /E   =(127106Pa)(2m)/(200109Pa)    =0.00127m   =1.27mmHowtocalculateradialcontractionThermalstressandforceStrainEnergyStressinganobjectstoresenergyinit.ForanaxialloadtheenergystoredcanbeexpressedasU=1/2FndlwhereU=deformationenergy(J(Nm),ftlb)Young'sModulus-ModulusofElasticity(orTensileModulus)-Hooke'sLaw Mostmetalsdeformsproportionaltoimposedloadoverarangeofloads.StressisproportionaltoloadandstrainisproportionaltodeformationasexpressedwithHooke'sLaw.E=stress/strain  =σ/ε  =(Fn/A)/(dl/lo)                      (4)whereE=Young'sModulus(N/m2)(lb/in2,psi)ModulusofElasticity,orYoung'sModulus,iscommonlyusedformetalsandmetalalloysandexpressedinterms106lbf/in2,N/m2orPa.Tensilemodulusisoftenusedforplasticsandisexpressedinterms105lbf/in2orGPa.ShearModulusofElasticity-orModulusofRigidityG=stress/strain  =τ/γ  =(Fp/A)/(s/d)                                   (5)whereG=ShearModulusofElasticity-orModulusofRigidity(N/m2)(lb/in2,psi)τ =shearstress((Pa)N/m2,psi)γ=unitlessmeasureofshearstrainFp=forceparalleltothefaceswhichtheyactA=area(m2,in2)s=displacementofthefaces(m,in)d=distancebetweenthefacesdisplaced(m,in)Ductilevs.BrittlematerialsBulkModulusElasticityTheBulkModulusElasticity-orVolumeModulus-isameasureofthesubstance'sresistancetouniformcompression.BulkModulusofElasticityistheratioofstresstochangeinvolumeofamaterialsubjectedtoaxialloading.ElasticModuliElasticmoduliforsomecommonmaterials:MaterialYoung'sModulus-E-ShearModulus-G-BulkModulus-K-(GPa)(106psi)(GPa)(106psi)(GPa)(106psi)Aluminum702470Brass913661Copper11042140Glass552337Iron9170100Lead165.67.7Steel200841601GPa=109Pa(N/m2)106psi=1Mpsi=103ksiSponsoredLinksRelatedTopicsMechanics-Forces,acceleration,displacement,vectors,motion,momentum,energyofobjectsandmore.Statics-Loads-forcesandtorque,beamsandcolumns.RelatedDocumentsEngineeringMaterials-Sometypicalpropertiesofengineeringmaterialslikesteel,plastics,ceramicsandcomposites.Hooke'sLaw-Hooke'slaw-force,elongationandspringconstant.Malleabilityvs.Brittlenesvs.Ductility-Plasticdeformationproperties.MetalsandAlloys-BulkModulusElasticity-TheBulkModulus-resistancetouniformcompression-forsomecommonmetalsandalloys.MetalsandAlloys-Young'sModulusofElasticity-ElasticpropertiesandYoung'smodulusformetalsandalloyslikecastiron,carbonsteelandmore.ModulusofRigidity-ShearModulus(ModulusofRigidity)istheelasticitycoefficientforshearingortorsionforce.Poisson'sRatio-Whenamaterialisstretchedinonedirectionittendstogetthinnerintheothertwodirections.Poisson'sRatiosMetals-SomemetalsandtheirPoisson'sRatios.ProcessPipes-AllowableStressvs.Temperature-AllowablewallstressinpipesaccordingASMEM31.3.RestrictedThermalExpansion-ForceandStress-Stressandforcewhenthermalexpansionapipe,beamorsimilarisrestricted.RotatingBodies-Stress-Stressinrotatingdiscandringbodies.SteamBoilerShells-Stressvs.BoilerPressure-Calculatethestressinsteamboilershellscausedbysteampressure.Steels-EnduranceLimitsandFatigueStress-Endurancelimitsandfatiguestressforsteels.Stress-Stressisforceappliedoncross-sectionalarea.StressinThick-WalledCylindersorTubes-Radialandtangentialstressinthick-walledcylindersortubeswithclosedends-withinternalandexternalpressure.StressinThin-WalledCylindersorTubes-Hoopandlongitudinalstressthin-walledtubesorcylinders.StructuralLumber-Properties-Propertiesofstructurallumber.ThreadedBolts-StressArea-Threadedboltstensilestressarea.ThreadedRods-LoadsinImperialUnits-Weightratingofthreadedhangerrods.Young'sModulus,TensileStrengthandYieldStrengthValuesforsomeMaterials-Young'sModulus(orTensileModulusalt.ModulusofElasticity)andUltimateTensileStrengthandYieldStrengthformaterialslikesteel,glass,woodandmanymore. 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